Search results for "integral transform"
showing 10 items of 18 documents
Regularity of the solution to a class of weakly singular fredholm integral equations of the second kind
1979
Continuity and differentiability properties of the solution to a class of Fredholm integral equations of the second kind with weakly singular kernel are derived. The equations studied in this paper arise from e.g. potential problems or problems of radiative equilibrium. Under reasonable assumptions it is proved that the solution possesses continuous derivatives in the interior of the interval of integration but may have mild singularities at the end-points.
A generalized integration formula for indefinite integrals of special functions
2020
An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...
Determination of relaxation and retardation spectrum by inverse functional filtering
2010
Abstract The article is devoted for the determination of the relaxation and retardation spectrum (RRS) from monotonic time- and frequency-domain material functions by the inverse functional filters executing discrete convolution algorithms for geometrically spaced data. It is shown that the problem of RRS determination from a wide variety of material functions leads to the three inverse filtering tasks on a logarithmic time or frequency scale with the three specific frequency responses concerning: (i) the time-domain functions, (ii) the real parts and (iii) the imaginary parts of the frequency-domain functions, and three algorithms (having the versions with even and odd number of coefficien…
Henstock type integral in harmonic analysis on zero-dimensional groups
2006
AbstractA Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.
Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
2015
The theory of HenstockâKurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
Inversion formulae for the integral transform on a locally compact zero-dimensional group
2009
Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.
Digital signal processing for relaxation data conversion
2005
Abstract The origins, philosophy and basic practical aspects are considered for an approach of digital data transformations for broadband dielectric relaxation spectroscopy and other relaxation experiments carrying out direct and inverse integral transforms with kernels depending on the ratio or product of arguments. The approach is based on the concept that the mentioned data transformations represent a filtering problem on a logarithmic scale allowing one to implement the transforms by digital functional filters with the logarithmic sampling. As an example, digital Kramers–Kronig transformers are considered.
On the translation of the three fundamental problems of elastic equilibrium of anisotropic bodies into systems of Fredholm first kind integral equati…
1972
Heuristic Algorithm for the Analysis of Fast Field Cycling (FFC) NMR Dispersion Curves
2021
Evaluation of nuclear magnetic relaxation dispersion (NMRD) curves obtained by the fast field cycling nuclear magnetic resonance (FFC-NMR) relaxometry technique is a valuable tool for analyzing the microscopic dynamics of condensed matter systems. However, quantitative data analysis involves several conceptual and practical issues. Moving forward from previous literature approaches, we propose a new analysis method, relying on the elaboration of the inverse integral transform of the NMRD curve. Our approach results in a true heuristic method, able to unambiguously individuate the dynamic domains in the system, thereby avoiding the possible introduction of any element of discretion. The anal…